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A lake is 20 m deep; its bottom stays at a constant 4 C while the air above is held at -10 C. The thermal conductivity of ice is 4 times that of water. Ignoring the expansion of water on freezing, what is the maximum thickness the ice layer can reach in steady state?

1. 20/11 m
2. 200/11 m
3. 20 m
4. 10 m

Correct answer: 200/11 m

Solution

Setting equal heat currents through the ice (conductivity 4K, drop 10 C) and the underlying water (conductivity K, drop 4 C) gives 40/x = 4/(20 - x), whose solution is x = 200/11 m.

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